Efficient Estimation of Mean Ability Growth Using Vertical Scaling

ABSTRACT In recent years, the interest in measuring growth in student ability in various subjects between different grades in school has increased. Therefore, good precision in the estimated growth is of importance. This paper aims to compare estimation methods and test designs when it comes to precision and bias of the estimated growth of mean ability between two groups of students that differ substantially. This is performed by a simulation study. One- and two-parameter item response models are assumed and the estimated abilities are vertically scaled using the non-equivalent anchor test design by estimating the abilities in one single run, so-called concurrent calibration. The connection between the test design and the Fisher information is also discussed. The results indicate that the expected a posteriori estimation method is preferred when estimating differences in mean ability between groups. Results also indicate that a test design with common items of medium difficulty leads to better precision, which coincides with previous results from horizontal equating.